Okay I have an idea of the solution but would need more information about your rental.
The state city and zip would be helpful as in knowing that I could compare comps to what you are providing. Are you saying that every person in that zip code is on food stamps? Every place for rent is icky and no one would want to live there but only those forced into that zip code will live there? Are there no nice places in that zip code at all?
The basic plan for your situation due to California law is simple. Raise the income criteria to 6X the income afer taxes, take home i.e. net. :)
They way I am thinking of this is more like a flow chart. In my flow chart there are several bubbles needing answers prior to offering a showing.
The first bubble is income. Second, but no less important is credit score.
Again combining income to get the 3X is a wrong philosophy, in my opinion. If you do or are forced to combine incomes then I really think you should be sure that if one moves out the other will have no problem carring the lease on there own until you and tenant have found a replacement roomate.
Unless you are doing a communal living situation of which I am not knocking. If that is your market and you do it correctly then you also win. Anyone who is sucessful in this senario is screening in some manner i.e. co-signers.